Question

This is the graph of y = sin(x). Does anyone know the second part?

Answer 1

Answers for whole assignment:

(starting after this question)

2) graph 2

3) Minimum: -4

Maximum: 4

Amplitude: 4

zeros: 2nd and 3rd option

4) 2nd graph

5) range of y = sin(x)?

1st one

range of y = 3sin(x)?

2nd one

range of y = –3sin(x)?

2nd one

range of y = –3sin(x) – 2?

3rd one

6) graph 1

7) graph 3

8) amplitude = 2

midline y = 4

3rd option

9) 2nd option

10) The graph of y = –2sin(x) – 1 is the graph of the parent function stretched vertically by a factor of 2, reflected over the x-axis, and shifted 1 unit down. The maximum of the parent function is 1, the minimum is –1, and the amplitude is 1. The maximum of y = –2sin(x) – 1 is 1, the minimum is –3, and the amplitude is 2.

Answer 2

The resulting graph is
`y = 5\cdot \sin x`.

Explanation:

The resulting function is of the form:

`y = A\cdot \sin x + k`

Where:

`x` - Independent variable, dimensionless.

`y` - Dependent variable, dimensionless.

`A` - Amplitude, dimensionless.

`k` - Midpoint value, dimensionless.

The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is:
`A > 0`. According to the graph, the function is bounded between 5 (
`y_(max)`) and -5 (
`y_(min)`), and the midpoint value (
`k`) is 0. The amplitude is determined by the following calculation:

`A = (y_(max)-y_(min))/(2)`

If
`y_(min) = -5` and
`y_(max) = 5`, then:

`A = 5`

The resulting graph is
`y = 5\cdot \sin x`.